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Comment by stevage

2 days ago

You also learn about other pairings now being impossible.

No, that doesn't make sense either. For a truth booth, you're taking all the possible pairing arrangements, and dividing them into two sets. After the answer, one of those two sets is false. There is no way that this can provide more than 1 bit of information.

The match-ups can however give more information, as it isn't giving a yes/no answer.